Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -24}$ ${2x+3y = 28}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x-2y = -24}\thinspace$ to find $x$ ${-2x - 2}{(4)}{= -24}$ $-2x-8 = -24$ $-2x-8{+8} = -24{+8}$ $-2x = -16$ $\dfrac{-2x}{{-2}} = \dfrac{-16}{{-2}}$ ${x = 8}$ You can also plug ${y = 4}$ into $\thinspace {2x+3y = 28}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(4)}{= 28}$ ${x = 8}$